The two major galleries are the Uffizzi and Academia.
Neither is to be missed (IMHO), but the Uffizzi is huge
(Louvre class) and can easily consume an entire day.
If you're not an art lover, you might negotiate a
"Uffizzi highlights" with your travelling companions,
and then go and explore other things. The Academia,
is smaller, and worth seeing in its entirety.